Molecular collision density

Molecular rearrangement resulting from molecular collisions or excitation by light can be described with time-dependent many-electron density operators. The initial density operator can be constructed from the collection of initially (or asymptotically) accessible electronic states, with populations wj. In many cases these states can be chosen as single Slater determinants formed from a set of orthonormal molecular spin orbitals (MSOs) im as / =... 

As molecular density decreases, the average distance traveled between molecular collisions increases. 

The first possibility is that the attractive potential associated with the solid surface leads to an increased gaseous molecular number density and molecular velocity. The resulting increase in both gas-gas and gas-wall collision frequencies increases the T1. The second possibility is that although the measurements were obtained at a temperature significantly above the critical temperature of the bulk CF4 gas, it is possible that gas molecules are adsorbed onto the surface of the silica. The surface relaxation is expected to be very slow compared with spin-rotation interactions in the gas phase. We can therefore account for the effect of adsorption by assuming that relaxation effectively stops while the gas molecules adhere to the wall, which will then act to increase the relaxation time by the fraction of molecules on the surface. Both models are in accord with a measurable increase in density above that of the bulk gas. 

In conclusion, for condensed phases molecular rotations have quite a short lifetime, because of collisions. The eventual oscillations induced by the electric field are then dissipated in the liquid state leading to vibration. At collision densities corresponding to liquids the frequency of the collisions become comparable with the frequency of a single rotation, and because the probability of a change in rotational state on collision is high, the time a molecule exists in a given state is small. It is, therefore, obvious that the electric field cannot induce organization in condensed phases such as in the liquid state. 

In conduction, heat is conducted by the transfer of energy of motion between adjacent molecules in a liquid, gas, or solid. In a gas, atoms transfer energy to one another through molecular collisions. In metallic solids, the process of energy transfer via free electrons is also important. In convection, heat is transferred by bulk transport and mixing of macroscopic fluid elements. Recall that there can be forced convection, where the fluid is forced to flow via mechanical means, or natural (free) convection, where density differences cause fluid elements to flow. Since convection is found only in fluids, we will deal with it on only a limited basis. Radiation differs from conduction and convection in that no medium is needed for its propagation. As a result, the form of Eq. (4.1) is inappropriate for describing radiative heat transfer. Radiation is... 

Content. After a brief overview of molecular collisions and interactions, dipole radiation, and instrumentation (Chapter 2), we consider examples of measured collision-induced spectra, from the simplest systems (rare gas mixtures at low density) to the more complex molecular systems. Chapter 3 reviews the measurements. It is divided into three parts translational, rototranslational and rotovibrational induced spectra. Each of these considers the binary and ternary spectra, and van der Waals molecules we also take a brief look at the spectra of dense systems (liquids and solids). Once the experimental evidence is collected and understood in terms of simple models, a more theoretical approach is chosen for the discussion of induced dipole moments (Chapter 4) and the spectra (Chapters 5 and 6). Chapters 3 through 6 are the backbone of the book. Related topics, such as redistribution of radiation, electronic collision-induced absorption and emission, etc., and applications are considered in Chapter 7. 

Kolev [46] discussed the validity of these relations for fluid particle collisions considering the obvious discrepancies resulting from the different nature of the fluid particle collisions compared with the random molecular collisions. The basic assumptions in kinetic theory that the molecules are hard spheres and that the collisions are perfectly elastic and obey the classical conservation laws do not hold for real fluid particles because these particles are deformable, elastic and may agglomerate or even coalescence after random collisions. The collision density is thus not really an independent function of the coalescence probability. For bubbly flow Colella et al [15] also found the basic kinetic theory assumption that the particles are interacting only during collision violated, as the bubbles influence each other by means of their wakes. 

Besides active research he very much enjoys teaching. In the Physical-Technical Institute of Moscow he taught (1966-1992) general courses on Molecular Dynamics and Chemical Kinetics. In the Technion (since 1992) he has taught and still teaches graduate courses on different subjects Advanced Quantum Chemistry, Theory of Molecular Collisions, Kinetic Processes in Gases and Plasma, Theory of Fluctuations, Density Matrix Formalisms in Chemical Physics etc. 

For gas molecules, the heat capacity is a constant equal to C = (n/2)pkB where n is the number of degrees of freedom for molecule motion, p is the number density, and kB is the Boltzmann constant. The rms speed of molecules is given as v = V3kBTlm, whereas the mean free path depends on collision cross section and number density as = (pa)-1. When they are put together, one finds that the thermal conductivity of a gas is independent of p and therefore independent of the gas pressure. This is a classic result of kinetic theory. Note that this is valid only under the assumption that the mean free path is limited by inter-molecular collision. 

Molecular motors enter the model implicitly by specifying the interaction rules between two rods. Since the diffusivity of molecular motors is about 100 times larger than that of microtubules, as a first approximation we neglect spatial variations of the molecular motor density. While the varying concentration of molecular motors affects certain quantitative aspects [7], our analysis captures salient features of the phenomena and the collision rules are spatially homogeneous. All rods are assumed to be of equal length I and diameter d I,... 

---